Write an expression to describe the sequence below, and then find the 9th term. Use n to represent the position of a term in the sequence, where n = 1 for the first term.
–3, –6, –9, –12, ...
The expression to describe the sequence is n(-3). To find the 9th term, we substitute n = 9 into the expression:
9(-3) = -27
Therefore, the 9th term of the sequence is -27.
The sequence is arithmetic with a common difference of -3.
To describe the sequence, we can use the formula:
a(n) = a(1) + (n-1)d
where a(n) represents the nth term, a(1) is the first term, n is the position of the term, and d is the common difference.
In this case, the first term is -3 and the common difference is -3.
Plugging in the values, we get:
a(n) = -3 + (n-1)(-3)
To find the 9th term, we substitute n = 9 into the formula:
a(9) = -3 + (9-1)(-3)
= -3 + (8)(-3)
= -3 + (-24)
= -27
Therefore, the 9th term of the sequence is -27.